Re: The state of education in the USA.

On Apr 4, 3:54 pm, tgdenn...@xxxxxxxxxxxxx wrote:
On Apr 4, 1:21 pm, Tim Norfolk <timsn...@xxxxxxx> wrote:





On Apr 4, 11:21�am, tgdenn...@xxxxxxxxxxxxx wrote:


Actually, that isn't what you said.

What isn't what I said???


My apologies. I was responding to a sentence of yours that appeared in
an earlier message, to wit: "Why *should* our kids go
into science and engineering---or even become quality teachers, who
are treated even worse?"

My point is that this treatment is not universal in the US.,




An interesting assertion. I have been part of studies involving
technology and its effects in education for about 20 years.

"You have been part of" meaning you were studied or you were a
researcher who published the study?

I have worked on both sides - as the one trying to implement new
ideas, and as the one functioning as a control. I have not bothered to
publish in the area myself.


In many
such experiments, the immediate results showed that with self-selected
students using new technology (say, graphing calculators), the results
in specific courses looked better. Many of those gains did not carry
through to higher-level material, including abstract mathematics
courses, where low-level algebra skills are used less. In addition, as
those same techniques were applied to the general population, the
results always were that the novelty effect wore off, and the
standards declined.

I would be interested in some more detail on these studies. What
courses are you talking about (abstract mathematics)?  I also don't
get what you mean "applying the same techniques to the general
population".

Courses like Discrete Mathematics, Abstract Algebra, Advanced
Calculus, Linear Algebra and the like. Much of what is done there
involves some basic Algebra, with ideas from Calculus and Linear
Algebra. Without an understanding of variables and functions,
initially gained in Algebra I, no student can understand what is going
on. The same is true in any reasonable programming course. The latter
have been poisoned, so my colleagues tell me, by the web, as students
search for code to steal, rather than learning to write it themselves.

Since I don't follow this area closely, you will have to check the
literature yourself. The effect I am talking about is the well-known
one of novelty. When the new graphing calculators appeared, only the
"nerds" wanted one, and signed up for the courses where we tried out
their capabilities. Once they became part of the standard schoolbox,
interest in them wore off, and our students can do less with them than
I can do with pen and paper.


It doesn't bother me at all, since I don't expect that a non-
representative sample (SAT takers in the past) is going to predict the
results for the current population. I would be truly surprised if the
results *didn't* have to be re-normed, and down.

That might be true in some cases. But virtually every student in Ohio
who intends to go to higher education takes the ACT, and those
averages have gone down every single time, once the re-norming is
taken into account. This despite 60+ years of 'improvements' from the
Colleges of Education. If the life expectancy dropped by 5% every few
years, we'd be hanging doctors from the trees.




Once again, what you are saying is kind of vague. Can you be more
specific, or perhaps give an online reference to these studies you
keep talking about?


See the above. Without a lot of rote knowledge of basic arithmetic,
algebra becomes hard to follow, no matter what technology is used. In
that case, the underlying ideas of variables and functions become
meaningless, and inapplicable. There is some good evidence that, if
the abstract process engendered by learning algebra (see Piaget) is
not accomplished by a certain age, it will never be acquired. This is
similar to the tragic cases of humans who have never been exposed to
speech by age 8 or so, and do not have the brain connections that make
speech possible - ever.

The mathematical education community awaits your great expertise and
wisdom, but consider the following

1. Mathematics is the only subject to have been consistently taught
for about 2,500 years
2. In mathemaqtics, that which doesn't work is tossed onto the trash
heap, or given only a passing reference as a failed idea, or one
supplanted
3. Euclid's answer to King Ptolemy, who was bored by his lessons
"There is no royal road to geometry (mathematics)".

In short, I have yet to see one single innovation in mathematics
education that left students better prepared for further study. If you
have, let's see your evidence. From my experience, it takes properly-
prepared students with a willingness to work harder than in the non-
science disciplines. If you honestly have the magic bullet, you could
get a bunch of money from Bill Gates, and pretty much every major
corporation, since most post-graduate management programs include a
screening test of 8th-grade mathematics.
-tg



Teaching
students to push buttons, which is what much of the new technology
inevitably does, is no more useful than teaching golf by watching it
on TV - perhaps the next trend in education to reduce phys. ed.?

Most people who I have seen complain about mathematics education
weren't good at it, and extrapolate their ineptitude in the subject
(and current success) to 'mathematics is taught wrong', or
'mathematics is useless'. All I generally answer is that most of the
neat technology that they take for granted, including every aspect of
computers, imaging systems (MRI, CAT and PET scans), cell phones, and
modern pharmaceuticals, are only possible because of massive amounts
of mathematical modelling. To take imaging as one example, they seem
to think that the methods were invented by some MD puttering around,
when the truth is that the basic ideas incorporated deep mathematics
and physics, including Fourier transforms, and some incredible
software, the work of teams of mathematicians, physicists and
engineers. My own advisor worked on the first electronic computers,
helping to design the reactors for the Nautilus-class submarines that
kept America safe during the Cold War.

Because the average American takes such things for granted, and even
attacks the 'nerds' in the education system, we have fallen to at best
second place in most technology, and leads to at least some of our
economic woes.

.